一个最佳常数因子联系Gamma函数的全平面Hilbert型积分不等式

摘要

通过引入独立参量与指数函数中间变量,应用权函数的方法,建立一个最佳常数因子联系Gamma函数的全平面Hilbert型积分不等式,并考虑其等价式及特殊参数下的齐次与非齐次式.%By introducing independent parameters and intermediate variables of exponential function, and using the method of the weight functions,we established a Hilbert-type integral inequality in the whole plane related to the Gamma function of the best constant factor,and considered the equivalent forms,homogeneous and non-homogeneous forms under particular parameters.